An Introduction to Complex Systems Science and its Applications

Abstract

The standard assumptions that underlie many conceptual and quantitative frameworks do not hold for many complex physical, biological, and social systems. Complex systems science clarifies when and why such assumptions fail and provides alternative frameworks for understanding the properties of complex systems. This review introduces some of the basic principles of complex systems science, including complexity profiles, the tradeoff between efficiency and adaptability, the necessity of matching the complexity of systems to that of their environments, multi-scale analysis, and evolutionary processes. Our focus is on the general properties of systems as opposed to the modeling of specific dynamics; rather than provide a comprehensive review, we pedagogically describe a conceptual and analytic approach for understanding and interacting with the complex systems of our world. With the exception of a few footnotes, this paper assumes only a high school mathematical and scientific background, so that it may be accessible to academics in all fields, decision-makers in industry, government, and philanthropy, and anyone who is interested in systems and society.

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• Multiscale complexity of two-dimensional Ising systems with short-range, ferromagnetic interactions